Low earth orbit target orbit determination method and device

Abstract

The application discloses a low-orbit target orbit determination method and device, and relates to the technical field of orbit determination, and can be used for improving the accuracy and stability of low-orbit target orbit determination.

Description

Technical Field

[0001] The present invention relates to the field of aerospace dynamics technology, and in particular to a method and device for determining the orbit of a low-orbit target. Background Art

[0002] Existing space-based initial orbit determination technologies usually invert the target orbit based on limited observation data. For example, the existing technical solution uses the Laplace orbit determination method as a means of generating initial values, and further combines it with the Gooding method to solve the orbit parameters to obtain a more accurate orbit determination result. Another technical solution is to select multiple sets of observation data at different times for a single observation arc and call the Gooding method to perform orbit determination operations respectively, and by comparing and analyzing multiple orbit determination results, select the optimal solution or perform weighted processing on the orbit determination results to obtain a stable orbit determination output. In addition, the existing technology also proposes to construct an objective function, traverse the slant range parameters at the start and end times, set a threshold in multiple objective function values, and select the results that meet the conditions for averaging processing to obtain the initial orbit information of the target.

[0003] However, these existing technical solutions still have certain drawbacks in practical applications. For example, some rely on traversal calculations or optimization algorithms during the solution process, resulting in low computational efficiency. Alternatively, under short-arc observation conditions, some technologies may suffer from non-unique orbital solutions, making it difficult to accurately identify the true orbital solution.

[0004] This section is intended to provide a background or context to the embodiments of the invention that are recited in the claims. No statement herein is admitted to be prior art by virtue of its inclusion in this section. Summary of the Invention

[0005] An embodiment of the present invention provides a low-orbit target orbit determination method for determining target orbit parameters based solely on observation data at different times without requiring initial values ​​and in the presence of perturbation errors, thereby improving the accuracy and stability of low-orbit target orbit determination.

[0006] The low-orbit target orbit determination method includes:

[0007] Acquire observation data at different times; wherein the observation data includes: a first position vector of the observation platform relative to the center of the earth and a second position vector of the target relative to the observation platform;

[0008] Determining a target position vector based on the observation data and a pre-established target position relationship model; the target position vector includes a first target position vector corresponding to an initial observation time, a second target position vector corresponding to an intermediate observation time, and a third target position vector corresponding to a final observation time; the target position relationship model is determined based on the second target position vector and the first position vector;

[0009] The predicted target trajectory is determined based on the initial observation time, the first target position vector, the termination observation time and the third target position vector.

[0010] In some embodiments, determining the target position vector based on the observation data and a pre-established target position relationship model includes:

[0011] Determining a first distance of the target relative to the center of the earth at an intermediate observation moment based on the target position relationship model;

[0012] determining a third distance based on the first distance, a second distance of the observation platform relative to the center of the earth at the intermediate observation moment, an angle between the target and a line connecting the center of the earth and the observation platform, the first position vector, and a weight factor;

[0013] The target position vector is determined according to the first position vector, the second position vector, and the third distance.

[0014] In some embodiments, determining the first distance of the target relative to the center of the earth at the intermediate observation moment based on the target position relationship model includes:

[0015] Determining a normalized scale adjustment factor and an observation decoupling proportional coefficient based on the observation data;

[0016] Determining a first orbital structure coefficient, a second orbital structure coefficient, and a third orbital structure coefficient according to the normalized scale adjustment factor and the observation decoupling proportional coefficient;

[0017] The first distance is determined according to the first track structure coefficient, the second track structure coefficient, the third track structure coefficient and the target position relationship model.

[0018] In some embodiments, the third distance includes: a fourth distance of the target relative to the observation platform at the initial observation time, a fifth distance of the target relative to the observation platform at the intermediate observation time, and a sixth distance of the target relative to the observation platform at the end observation time; the weight factor includes a first weight factor and a second weight factor;

[0019] Determining the third distance according to the first distance, the second distance, the angle between the target and a line connecting the center of the earth and the observation platform, the first position vector, and a weight factor includes:

[0020] determining the fifth distance based on the first distance, the second distance, and an angle between the target and a line connecting the center of the earth and the observation platform;

[0021] The fourth distance and the sixth distance are determined according to the first position vector, the second position vector, the first weight factor, the second weight factor, and the fifth distance.

[0022] In some embodiments, determining the predicted target trajectory based on the initial observation time, the first target position vector, the termination observation time, and the third target position vector includes:

[0023] Determining target orbit parameters according to the initial observation time, the first target position vector, the termination observation time, and the third target position vector;

[0024] Perturbation compensation processing is performed based on the target orbit parameters to obtain a predicted target orbit.

[0025] In some embodiments, determining the target orbit parameters according to the initial observation time, the first target position vector, the termination observation time, and the third target position vector includes:

[0026] Determining initial orbit parameters according to the initial observation time, the first target position vector, the termination observation time, and the second target position vector;

[0027] Determine a target direction prediction value corresponding to the intermediate observation time according to the initial orbit parameters, and compare the target direction prediction value with the unit position vector of the observation platform at the intermediate observation time;

[0028] If the error between the target direction prediction value and the unit position vector of the observation platform at the intermediate observation time exceeds a preset threshold range, the target orbit parameter is determined according to the target direction prediction value.

[0029] In some embodiments, determining the target orbit parameter according to the target direction prediction value includes:

[0030] Establishing a nonlinear track model based on the target direction prediction value to obtain an optimized fourth distance and a sixth distance;

[0031] Optimized target orbit parameters are determined based on the optimized fourth distance and sixth distance.

[0032] In some embodiments, performing perturbation compensation based on the target orbit parameters to obtain a predicted target orbit includes:

[0033] Perturbation compensation is performed based on the optimized target orbit parameters, two-body dynamics model and J2 perturbation dynamics model to obtain the perturbation error;

[0034] determining a perturbation deviation according to the optimized third distance and its corresponding perturbation error;

[0035] determining a corrected second position vector according to the perturbation deviation and the second position vector;

[0036] performing orbit determination based on the corrected second position vector;

[0037] The above steps are iterated until the preset number of times is reached or convergence is achieved, and the corrected target orbit parameters are obtained.

[0038] In some embodiments, performing perturbation compensation according to the optimized target orbit parameters, the two-body dynamics model, and the J2 perturbation dynamics model to obtain the perturbation error includes:

[0039] Determine the velocity vector at the initial observation time according to the optimized target orbit parameters;

[0040] Based on the velocity vector at the initial observation time and its corresponding position vector, the two-body dynamics model and the J2 perturbation dynamics model, numerical integration is performed to obtain the predicted target position vector at different observation times and the J2 perturbation predicted target position vector;

[0041] A perturbation error is determined based on the predicted target position vector and the J2 perturbation predicted target position vector.

[0042] An embodiment of the present invention also provides a low-orbit target orbit determination device, which is used to accurately determine target orbit parameters based only on observation data at different times without the need for initial values ​​and in the presence of perturbation errors, thereby improving the accuracy and stability of low-orbit target orbit determination.

[0043] The low-orbit target orbit determination device includes:

[0044] An observation data acquisition module, configured to acquire observation data at different times; wherein the observation data includes: a first position vector of the observation platform relative to the center of the earth and a second position vector of the target relative to the observation platform;

[0045] a target position calculation module, configured to determine a target position vector based on the observation data and a pre-established target position relationship model; the target position vector comprising a first target position vector corresponding to an initial observation time, a second target position vector corresponding to an intermediate observation time, and a third target position vector corresponding to a final observation time; the target position relationship model being determined based on the second target position vector corresponding to the intermediate observation time and the first position vector;

[0046] The orbit prediction module is used to determine the predicted target orbit based on the initial observation time, the first target position vector, the end observation time and the third target position vector.

[0047] An embodiment of the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the above-mentioned low-orbit target orbit determination method is implemented.

[0048] An embodiment of the present invention further provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the above-mentioned low-orbit target orbit determination method is implemented.

[0049] An embodiment of the present invention further provides a computer program product, which includes a computer program. When the computer program is executed by a processor, it implements the above-mentioned low-orbit target orbit determination method.

[0050] The low-orbit target orbit determination method and apparatus provided by embodiments of the present invention utilizes position information of the observation platform and the target direction at multiple observation times to construct a target position relationship model. The target position vector is extracted at the initial and final observation times, and the difference is calculated based on observation data from intermediate observation times to form three-point target position information. The target's initial orbit is then accurately inferred using an orbit inversion model. Compared to traditional orbit determination methods that rely on high-precision initial estimates and are susceptible to observation errors, this solution offers greater robustness and adaptability. Because this method introduces position constraints at intermediate observation times during model building, it improves the stability and reliability of the orbit inference results. This approach is particularly suitable for space applications with short observation times or low observation accuracy. This technical solution significantly reduces reliance on high-precision initial values, helping to improve orbit determination efficiency and system resource utilization, and meeting the engineering requirements of large-scale observations and automated processing. The server-executed low-orbit target orbit determination method effectively achieves efficient preliminary determination of the trajectory of low-orbit space targets without relying on traditional initial value estimates. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0052] Figure 1A Schematic diagram of space-based observation in an embodiment of the present invention;

[0053] Figure 1B 1 is a flow chart of a method for determining the orbit of a low-orbit target according to an embodiment of the present invention;

[0054] Figure 2 1 is a flow chart of a method for determining a low-orbit target orbit in another embodiment of the present invention;

[0055] Figure 3 1 is a flow chart of a method for determining a low-orbit target orbit in another embodiment of the present invention;

[0056] Figure 4 1 is a flow chart of a method for determining a low-orbit target orbit in another embodiment of the present invention;

[0057] Figure 5 1 is a flow chart of a method for determining a low-orbit target orbit in another embodiment of the present invention;

[0058] Figure 6 1 is a flow chart of a method for determining a low-orbit target orbit in another embodiment of the present invention;

[0059] Figure 7 1 is a flow chart of a method for determining a low-orbit target orbit in another embodiment of the present invention;

[0060] Figure 8 1 is a flow chart of a method for determining a low-orbit target orbit in another embodiment of the present invention;

[0061] Figure 9 1 is a flow chart of a method for determining a low-orbit target orbit in another embodiment of the present invention;

[0062] Figure 10A Schematic diagram of a camera pointing selection strategy according to an embodiment of the present invention;

[0063] Figure 10B A schematic diagram of a camera orientation selection strategy according to another embodiment of the present invention;

[0064] Figure 11 Schematic diagram of the structure of a low-orbit target orbit determination device in another embodiment of the present invention;

[0065] Figure 12 A schematic diagram of the physical structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0066] To make the purpose, technical solutions and advantages of the embodiments of the present invention more clear, the embodiments of the present invention are further described in detail below with reference to the accompanying drawings. Here, the exemplary embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0067] In order to improve the orbit determination accuracy and reduce the dependence on initial values ​​during the low-orbit target orbit determination process, this application proposes a low-orbit target orbit determination method to address the problems of strong dependence on initial values, susceptibility to observation error interference, and poor orbit solution stability in traditional orbit determination algorithms. Based on three sets of observation data, this application uses the Gaussian Method for Initial Orbit Determination to solve the target position vector without the need for initial values. By adopting the Lambert transfer algorithm to invert the initial orbit parameters and combining them with the Gooding orbit determination algorithm to iteratively optimize the initial orbit parameters, the final calculated orbital elements are close to the true orbit parameters. On this basis, the J2 perturbation dynamics model is further combined for target position prediction and error analysis, achieving systematic compensation for the solution results of the traditional two-body dynamics model.

[0068] Figure 1A Figure 1 is a schematic diagram of space-based observation. Figure 1A As shown, the geocentric inertial coordinate system (X i , Y i , Z i ), the target S is located in the Low Earth Orbit (LEO). The position vector of the target S relative to the center of the earth O is denoted as r i .

[0069] The observation platform P is an observation device used to obtain the spatial position of the target S. The observation platform P can be located on a spacecraft in low-Earth orbit, such as a satellite or probe, or on the ground. The position vector of the target S relative to the observation platform P is denoted as ρ i The position vector of the observation platform P relative to the center of the earth O is recorded as Rc i Among them, ρ i With Rc i The complementary angle between them is denoted as θ.

[0070] For example, multiple observation platforms P can be deployed on multiple satellites in a large-scale low-orbit communication constellation. For example, ten observation platforms P can be deployed. Each observation platform P is equipped with a camera device for capturing observation images of a target S in low-orbit space. The camera does not need to actively track the target S; it only records observation images of the target S within the camera's field of view. These observation images are processed using image processing techniques to extract observation data of the target S relative to the observation platform P. The camera's field of view has a 6° × 6° angle.

[0071] In order to reduce noise interference in the observation data, it is preferred to perform Savitzky–Golay (SG) filtering on the observation data extracted from the observation image before performing Gaussian orbit determination calculation.

[0072] The observation data includes the right ascension and declination information of the target S relative to the observation platform P in a discrete time series, and multiple data pairs collected at 0.1 second intervals within the observation arc. Each data pair includes: the position vector Rc of the observation platform P relative to the center of the earth O i , the unit position vector L of the target S relative to the observation platform P i and observation time t i In this embodiment, only the unit position vector L of the target S relative to the observation platform P in the data pair is calculated. i Perform SG filtering.

[0073] SG filtering is a smoothing method based on local polynomial least squares fitting. It smoothes the central data points by fitting a polynomial to the observed data within a sliding window.

[0074] Specifically, the present application performs SG filtering by calling the savgol_filter function of the scipy.signal module in Python. The input data of the savgol_filter function include: the unit position vector L of the target S relative to the observation platform P i , data window size (preferably 111) and the polynomial order used for local fitting (preferably 4).

[0075] When performing SG filtering, for each data point, n data points are selected from both sides of the data point to construct a local sliding window, forming a window interval with a total width of 2n+1. For data points close to the data boundary, if it is not possible to select n data points from both sides of the data point, 2n+1 data points can be selected from one side of the data point. Taking the total width of the local sliding window as 5 (n=2) as an example, the local fitting data points include: x i-2 、x i-1 、x i 、x i+1 and x i+2 .

[0076] In the above local sliding window, data fitting is performed based on the set k-order polynomial. For example, the quadratic polynomial can be used. Perform data fitting. Use the least squares method to find the coefficients of the k-th order polynomial, minimizing the squared error between the fitted curve and the original data points within the local sliding window. Replace the original data points with the value of the fitted k-th order polynomial at the center point (x = 0) to achieve data smoothing.

[0077] In one embodiment of the present application, a method for determining the orbit of a low-orbit target is provided, and the execution subject of the method is a server, such as Figure 1A and Figure 1B As shown, the low-orbit target orbit determination method includes steps 101 to 103.

[0078] Step 101: Acquire observation data at different times, wherein the observation data includes: the position vector of the observation platform P relative to the center of the earth O (i.e., the first position vector) and the unit position vector of the target S relative to the observation platform P (i.e., the second position vector).

[0079] Step 102: Determine the position vector of the observation platform P relative to the Earth's center O based on the observation data and a pre-established target position relationship model. The position vector of the observation platform P relative to the Earth's center O includes a first target position vector corresponding to the initial observation time t1, a second target position vector corresponding to the intermediate observation time t2, and a third target position vector corresponding to the final observation time t3. The target position relationship model is determined based on the second target position vector corresponding to the intermediate observation time t2 and the position vector of the observation platform P relative to the Earth's center O. The first target position vector is r1, the position vector of the target S relative to the Earth's center O at the initial observation time, the second target position vector is r2, the position vector of the target S relative to the Earth's center O at the intermediate observation time, and the third target position vector is r3, the position vector of the target S relative to the Earth's center O at the final observation time.

[0080] Step 103: Determine the predicted target trajectory based on the initial observation time t1, the first target position vector, the final observation time t3, and the third target position vector.

[0081] According to the above embodiment, the position information of the observation platform and the target direction at multiple observation times is used to construct a target position relationship model. The target position vector is extracted at the initial observation time and the final observation time, and the difference is solved by combining the observation data at the intermediate observation time to form three-point target position information. The initial orbit of the target is then accurately calculated through the orbit inversion model. Compared with traditional orbit determination methods that rely on high-precision initial estimates and are easily affected by observation errors, this solution has stronger robustness and adaptability. Because this method introduces position constraints at intermediate observation times during the model establishment process, the stability and reliability of the orbit calculation results are improved. It is particularly suitable for space application scenarios with short observation time or low observation accuracy. This technical solution significantly reduces the reliance on high-precision initial values, helps to improve orbit determination efficiency and system resource utilization, and adapts to the engineering requirements of large-scale observation and automated processing. The low-orbit target orbit determination method executed by the server effectively achieves efficient preliminary determination of the trajectory of low-orbit space targets without relying on traditional initial value estimates.

[0082] In the embodiment of the present invention, the observation times include: initial observation time t1, intermediate observation time t2, and final observation time t3. The observation data includes: position vector Rc1 of the observation platform P relative to the center of the earth O at the initial observation time, position vector Rc2 of the observation platform P relative to the center of the earth O at the intermediate observation time, and position vector Rc3 of the observation platform P relative to the center of the earth O at the final observation time; unit position vector L1 of the target S relative to the observation platform P at the initial observation time, unit position vector L2 of the target S relative to the observation platform P at the intermediate observation time, and unit position vector L3 of the target S relative to the observation platform P at the final observation time.

[0083] In some embodiments, as Figure 2 As shown, step 102 includes steps 201 to 203.

[0084] Step 201: Determine the distance r2 (ie, the first distance) of the target S relative to the center of the earth O at the intermediate observation moment based on the target position relationship model.

[0085] In the embodiment of the present invention, based on the Gauss orbit determination method, an algebraic equation is constructed to calculate the distance r2 of the target S relative to the center of the earth O at the intermediate observation time. The Gauss orbit determination method uses the position vector Rc of the observation platform P relative to the center of the earth O obtained at three different observation times. i and the unit position vector L of the target S relative to the observation platform P i , and combined with the orbital mechanics law of the target S between each observation time, an octave algebraic equation about r2 is derived as the target position relationship model. The coefficients in the octave algebraic equation are based on the observation time t i , the position vector Rc of the observation platform P relative to the center of the earth O i and the unit position vector L of the target S relative to the observation platform P i By numerically solving the octal algebraic equation, multiple candidate solutions can be obtained, from which positive real number solutions that meet the actual physical constraints are selected to determine the distance r2 of the target S relative to the center of the earth O at the intermediate observation time.

[0086] Step 202: Determine the distance of target S from observation platform P (i.e., the third distance) based on the distance r2 of target S from Earth's center O at the intermediate observation time, the distance Rc2 of observation platform P from Earth's center O at the intermediate observation time (i.e., the second distance), the angle θ between target S and the line connecting Earth's center O and observation platform P, the position vector of observation platform P relative to Earth's center O, and weighting factors. The distance of target S from observation platform P includes: the distance ρ1 of target S from observation platform P at the initial observation time, the distance ρ2 of target S from observation platform P at the intermediate observation time, and the distance ρ3 of target S from observation platform P at the final observation time. The weighting factors include: a first weighting factor λ1 and a second weighting factor λ3.

[0087] In the embodiment of the present invention, according to Figure 1A The spatial geometric relationship between the Earth's center O, target S, and observation platform P, shown in Figure 1, is combined with the angle formed between the line connecting target S and observation platform P and the line connecting Earth's center O and observation platform P to determine the distance of target S from observation platform P at the intermediate observation time. After obtaining the distance of target S from observation platform P at the intermediate observation time, a weighted interpolation method is further introduced to calculate the distance of target S from observation platform P at the initial observation time t1 and the final observation time t3 using the first weight factor λ1 and the second weight factor λ3, thereby obtaining the distance data of target S from observation platform P for the entire observation period.

[0088] Step 203: Determine the target position vector based on the position vector of the observation platform P relative to the Earth's center O, the unit position vector of the target S relative to the observation platform P, and the distance of the target S relative to the observation platform P. The target position vector includes: the position vector r1 of the target S relative to the Earth's center O at the initial observation time, the position vector r2 of the target S relative to the Earth's center O at the intermediate observation time, and the position vector r3 of the target S relative to the Earth's center O at the final observation time.

[0089] In the embodiment of the present invention, the position vector Rc1 of the observation platform P relative to the center of the earth O at the initial observation moment, the unit position vector L1 of the target S relative to the observation platform P at the initial observation moment, and the distance ρ1 of the target S relative to the observation platform P at the initial observation moment; the position vector Rc2 of the observation platform P relative to the center of the earth O at the intermediate observation moment, the unit position vector L2 of the target S relative to the observation platform P at the intermediate observation moment, and the distance ρ2 of the target S relative to the observation platform P at the intermediate observation moment; the position vector Rc3 of the observation platform P relative to the center of the earth O at the termination observation moment, the unit position vector L3 of the target S relative to the observation platform P at the termination observation moment, and the distance ρ3 of the target S relative to the observation platform P at the termination observation moment are substituted into the following formula (1) to calculate the position vector r1 of the target S relative to the center of the earth O at the initial observation moment, the position vector r2 of the target S relative to the center of the earth O at the intermediate observation moment, and the position vector r3 of the target S relative to the center of the earth O at the termination observation moment.

[0090]

[0091] Among them, r i is the position vector of the target S relative to the center of the earth O at any observation time, Rc i is the position vector of the observation platform P relative to the center of the earth O at any observation time, L i is the unit position vector of the target S relative to the observation platform P at any observation time, ρ i is the distance between the target S and the observation platform P at any observation time.

[0092] According to the above embodiment, by introducing a target position relationship model based on the Gauss orbit determination method, an octal algebraic equation is constructed using the observation platform position and target direction information obtained at three different observation times to accurately solve the distance of the target relative to the center of the earth at the intermediate observation time. The position vector of the observation platform relative to the center of the earth and the unit position vector of the target relative to the observation platform are further combined to infer the target's geocentric position vector at each observation time. Without requiring the target's initial velocity information, the above method effectively avoids the uncertainty caused by the dependence on the initial velocity value in traditional orbit determination methods. It can stably obtain the target's orbital state in the presence of actual observation errors, significantly improving the robustness and accuracy of low-orbit target orbit determination.

[0093] In some embodiments, as Figure 3 As shown, step 201 includes steps 301 to 303.

[0094] Step 301: Determine a normalized scale adjustment factor C and an observation decoupling proportional coefficient γ based on observation data. The observation data includes: the position vector Rc1 of the observation platform P relative to the Earth's center O at the initial observation time, the position vector Rc2 of the observation platform P relative to the Earth's center O at the intermediate observation time, the position vector Rc3 of the observation platform P relative to the Earth's center O at the final observation time, the unit position vector L1 of the target S relative to the observation platform P at the initial observation time, the unit position vector L2 of the target S relative to the observation platform P at the intermediate observation time, the unit position vector L3 of the target S relative to the observation platform P at the final observation time, the initial observation time t1, the intermediate observation time t2, and the final observation time t3.

[0095] In the embodiment of the present invention, the initial observation time t1, the intermediate observation time t2 and the final observation time t3 are substituted into the following formula (2) to calculate the time difference t between the observation times. 21 , t 31 and t 32 .

[0096]

[0097] Among them, t i and t j are observation times, t ij is the time interval between the corresponding observation times.

[0098] The directional vector volume factor V is calculated according to the following formula (3).

[0099]

[0100] Among them, L1 is the unit position vector of target S relative to the observation platform P at the initial observation moment, L2 is the unit position vector of target S relative to the observation platform P at the intermediate observation moment, and L3 is the unit position vector of target S relative to the observation platform P at the end of observation.

[0101] The second intermediate variable B is calculated according to the following formula (4).

[0102]

[0103] Where μ is the standard gravitational constant of the Earth’s center, t 21 , t 31 , t 32 are all time differences at the observation moments, L1 is the unit position vector of the target S relative to the observation platform P at the initial observation moment, L3 is the unit position vector of the target S relative to the observation platform P at the end of the observation moment, Rc1 is the position vector of the observation platform P relative to the center of the earth O at the initial observation moment, and Rc3 is the position vector of the observation platform P relative to the center of the earth O at the end of the observation moment.

[0104] The direction vector volume factor V, the time difference of observation time t 31 , the distance Rc2 of the observation platform P relative to the center of the earth O at the intermediate observation time and the second intermediate variable B are substituted into the following formula (5) to calculate the normalized scale adjustment factor C.

[0105]

[0106] Where V is the direction vector volume factor, t 31 is the time difference of the observation moments, Rc2 is the distance of the observation platform P relative to the center of the earth O at the intermediate observation moment (obtained by taking the modulus of the position vector Rc2 of the observation platform P relative to the center of the earth O at the intermediate observation moment), and B is the second intermediate variable.

[0107] The first intermediate variable A is calculated according to the following formula (6).

[0108]

[0109] Among them, Rc2 is the distance between the observation platform P and the center of the earth O at the intermediate observation time, L1 is the unit position vector of the target S relative to the observation platform P at the initial observation time, L3 is the unit position vector of the target S relative to the observation platform P at the end of the observation time, Rc1 is the position vector of the observation platform P relative to the center of the earth O at the initial observation time, Rc2 is the position vector of the observation platform P relative to the center of the earth O at the intermediate observation time, and Rc3 is the position vector of the observation platform P relative to the center of the earth O at the end of the observation time. 21 , t 31 , t 32 are the time differences of the observation times.

[0110] Substitute the first intermediate variable A and the second intermediate variable B into the following formula (7) to calculate the observation decoupling proportional coefficient γ.

[0111]

[0112] Among them, A is the second intermediate variable, and B is the second intermediate variable.

[0113] Step 302: Determine the first orbital structure coefficient C1, the second orbital structure coefficient C2, and the third orbital structure coefficient C3 according to the normalized scale adjustment factor C and the observation decoupling proportional coefficient γ.

[0114] In the embodiment of the present invention, the normalized scale adjustment factor C is substituted into the following formula (8) to calculate the first track structure coefficient C1.

[0115]

[0116] Among them, C is the normalized scale adjustment factor.

[0117] The distance Rc2 of the observation platform P relative to the center of the earth O at the intermediate observation time, the normalized scale adjustment factor C, the observation decoupling ratio coefficient γ, and Figure 1A The ρ shown i With Rc i Substitute the included angle θ between them into the following formula (9) to calculate the second track structure coefficient C2.

[0118]

[0119] Where Rc2 is the distance between the observation platform P and the center of the earth O at the intermediate observation time, C is the normalized scale adjustment factor, γ is the observation decoupling proportional coefficient, and θ is the complementary angle between ρ2 and Rc2 at the intermediate observation time.

[0120] The distance Rc2 of the observation platform P relative to the center of the earth O at the intermediate observation time, the normalized scale adjustment factor C, the observation decoupling ratio coefficient γ, and Figure 1A The ρ shown i With Rc i Substitute the angle θ between them into the following formula (10) to calculate the third track structure coefficient C3.

[0121]

[0122] Where Rc2 is the distance between the observation platform P and the center of the earth O at the intermediate observation time, C is the normalized scale adjustment factor, γ is the observation decoupling proportional coefficient, and θ is the complementary angle between ρ2 and Rc2 at the intermediate observation time.

[0123] Step 303: Determine the distance r2 of the target S relative to the center of the earth O at the intermediate observation time based on the first orbit structure coefficient C1, the second orbit structure coefficient C2, the third orbit structure coefficient C3 and the target position relationship model.

[0124] In the embodiment of the present invention, the target position relationship model is shown in the following formula (11):

[0125]

[0126] Among them, C1 is the first orbit structure coefficient, C2 is the second orbit structure coefficient, C3 is the third orbit structure coefficient, Rc2 is the distance of the observation platform P relative to the center of the earth O at the intermediate observation time, and r2 is the distance of the target S relative to the center of the earth O at the intermediate observation time.

[0127] Since the above octant polynomial has a set of real solutions (usually three positive real roots) at r2 = Rc2, this means that the distance of target S relative to the center of the Earth O at the intermediate observation time t2 is equal to the distance of the observation platform P relative to the center of the Earth O, and target S and observation platform P coincide in space. However, in actual physical scenarios, there is a non-zero relative spatial distance between the observation platform P and the observed target S. Therefore, although this real solution is mathematically valid, it has no practical significance in physics and is an invalid solution. In order to eliminate such invalid solutions and improve the stability and efficiency of the numerical solution, polynomial division is used to reduce the power of the above formula (11) to obtain the following formula (12).

[0128]

[0129] Substitute the first orbit structure coefficient C1, the second orbit structure coefficient C2, the third orbit structure coefficient C3 and the distance Rc2 of the observation platform P relative to the center of the earth O at the intermediate observation time into the above formula (12) to solve the distance r2 of the target S relative to the center of the earth O at the intermediate observation time.

[0130] According to the above embodiment, by introducing a normalized scale adjustment factor and an observation decoupling proportional coefficient, and combining multiple sets of observation data and their corresponding spatial geometric relationships, a high-order algebraic equation for solving the distance of the target relative to the center of the earth at the intermediate observation moment is constructed, and three orbital structure coefficients are derived based on the equation, thereby accurately describing the nonlinear relationship between the target position and the observation parameters. Furthermore, by reducing the power of the constructed octal algebraic equation, physically invalid mathematical solutions are effectively eliminated, and the convergence and stability of the numerical solution are improved. The above method achieves an accurate estimation of the position of the target relative to the center of the earth at the intermediate observation moment without relying on the initial velocity information of the target, and significantly enhances the adaptability and robustness to observation errors in the orbit inversion process.

[0131] In some embodiments, as Figure 4As shown, step 202 includes steps 401 and 402.

[0132] Step 401: Determine the distance ρ2 (i.e., the fifth distance) of the target S relative to the observation platform P at the intermediate observation moment based on the distance r2 of the target S relative to the center of the earth O at the intermediate observation moment, the distance Rc2 of the observation platform P relative to the center of the earth O at the intermediate observation moment, and the angle θ between the target S and the line connecting the center of the earth O and the observation platform P.

[0133] In the embodiment of the present invention, the distance r2 of the target S relative to the center of the earth O at the intermediate observation time obtained by the above formula (12) is substituted into the following formula (13) to calculate the distance ρ2 of the target S relative to the observation platform P at the intermediate observation time.

[0134]

[0135] Among them, r2 is the distance of the target S relative to the center of the earth O at the intermediate observation time, Rc2 is the distance of the observation platform P relative to the center of the earth O at the intermediate observation time, ρ2 is the distance of the target S relative to the observation platform P at the intermediate observation time, and θ is the complementary angle of the angle between ρ2 and Rc2 at the intermediate observation time.

[0136] Step 402: Determine the distance ρ1 (i.e., the fourth distance) of the target S relative to the observation platform P at the initial observation moment and the distance ρ3 (i.e., the sixth distance) of the target S relative to the observation platform P at the final observation moment based on the position vector of the observation platform P relative to the center of the earth O, the unit position vector of the target S relative to the observation platform P, the first weight factor λ1, the second weight factor λ3, and the distance ρ2 of the target S relative to the observation platform P at the intermediate observation moment.

[0137] In the embodiment of the present invention, t 32 and t 21 Substitute them into the following formula (14) to calculate the first position propagation coefficient f1 and the second position propagation coefficient f3.

[0138]

[0139] Among them, f i is the position propagation coefficient, μ is the standard gravitational constant of the Earth’s center, r2 is the distance of the target S relative to the Earth’s center O at the intermediate observation time, t i2 is the time interval between the intermediate observation time and each observation time, t i2 = -t 2i .

[0140] Then t 32 and t 21 Substitute them into the following formula (15) to calculate the first velocity propagation coefficient g1 and the second velocity propagation coefficient g3.

[0141]

[0142] Among them, g i is the velocity propagation coefficient, μ is the standard gravitational constant of the Earth’s center, r2 is the distance of the target S relative to the Earth’s center O at the intermediate observation time, t i2 is the time interval between the intermediate observation time and each observation time.

[0143] Substitute the first position propagation coefficient f1, the second position propagation coefficient f3, the first velocity propagation coefficient g1, and the second velocity propagation coefficient g3 into the following formula (16) to calculate the first weight factor λ1.

[0144]

[0145] Among them, g1 is the first velocity propagation coefficient, g3 is the second velocity propagation coefficient, f1 is the first position propagation coefficient, and f3 is the second position propagation coefficient.

[0146] Substitute the first position propagation coefficient f1, the second position propagation coefficient f3, the first velocity propagation coefficient g1 and the second velocity propagation coefficient g3 into the following formula (17) to calculate the second weight factor λ3.

[0147]

[0148] Among them, g1 is the first velocity propagation coefficient, g3 is the second velocity propagation coefficient, f1 is the first position propagation coefficient, and f3 is the second position propagation coefficient.

[0149] Furthermore, the distance ρ1 of the target S relative to the observation platform P at the initial observation time and the distance ρ3 of the target S relative to the observation platform P at the end observation time are calculated based on the following formula (18).

[0150]

[0151] Among them, Rc2 is the position vector of the observation platform P relative to the earth's center O at the intermediate observation moment, ρ2 is the position vector of the target S relative to the observation platform P at the intermediate observation moment, λ1 is the first weight factor, Rc1 is the position vector of the observation platform P relative to the earth's center O at the initial observation moment, ρ1 is the position vector of the target S relative to the observation platform P at the initial observation moment, λ3 is the second weight factor, Rc3 is the position vector of the observation platform P relative to the earth's center O at the end of the observation moment, and ρ3 is the position vector of the target S relative to the observation platform P at the end of the observation moment.

[0152] because , so the above formula (19) can be rewritten as follows:

[0153]

[0154] By cross-multiplying the two ends of formula (19) with the unit position vector L1 of the target S relative to the observation platform P at the initial observation time and the unit position vector L3 of the target S relative to the observation platform P at the final observation time, we obtain two linear equations about ρ1 and ρ3. Then, substitute the position vector Rc1 of the observation platform P relative to the center of the earth O at the initial observation time, the position vector Rc2 of the observation platform P relative to the center of the earth O at the intermediate observation time, the position vector Rc3 of the observation platform P relative to the center of the earth O at the final observation time, the unit position vector L1 of the target S relative to the observation platform P at the initial observation time, the unit position vector L2 of the target S relative to the observation platform P at the intermediate observation time, the unit position vector L3 of the target S relative to the observation platform P at the final observation time, the first weight factor λ1, the second weight factor λ3, and the distance ρ2 of the target S relative to the observation platform P at the intermediate observation time into the linear equations and solve them to obtain the distance ρ1 of the target S relative to the observation platform P at the initial observation time and the distance ρ3 of the target S relative to the observation platform P at the final observation time.

[0155] According to the above embodiment, by introducing observation data at different times and combining the spatial geometric relationship between the target and the observation platform, a target position relationship model is established. This allows the target's distance from the Earth's center at intermediate observation times to be accurately determined based on the target's unit position vector relative to the observation platform and the observation platform's position vector relative to the Earth's center, without relying on the target's initial velocity information. Furthermore, a weighted interpolation method combining orbital propagation coefficients and weight factors is used to estimate the target's distance from the observation platform and reconstruct its spatial position at each observation time. By constructing a target position relationship model and introducing a normalized scale adjustment factor and an observation decoupling proportional coefficient, the numerical stability of the orbit calculation and the physical feasibility of the solution are effectively improved. The use of a polynomial power reduction method effectively eliminates physically invalid solutions, enhancing the convergence and robustness of the calculation process. The Gaussian orbit determination method provided by the present invention has the advantages of high observation information utilization and low dependence on initial state, making it particularly suitable for applications such as deep space exploration missions and rapid orbit determination of targets in the early stages of an orbit.

[0156] In some embodiments, as Figure 10A and Figure 10B As shown in FIG, the octet algebraic equation for solving the distance between the target S and the relative center of the Earth O in the Gaussian orbit determination method usually has two real number solutions, corresponding to two possible target orbital positions.

[0157] like Figure 10A As shown, when the target S is located Figure 10A When the "Singular" singular curve is located, the two real solutions of the octic algebraic equation tend to coincide, that is, the distinguishability of the solutions is weakened. Figure 10AThe singular curves shown exhibit a closed hyperbolic structure, visually depicting the target's potential location in a singular region of orbital geometry where the solution fails. As the target S approaches this "singular" singular curve, the difference between the two real solutions decreases significantly, leading to an increase in the uncertainty of the solution.

[0158] like Figure 10B Figure 2 shows the simulation results of orbit measurements under different camera pointing strategies. At the 1.3Rc altitude layer (corresponding to the pink dashed arc in the figure), if the target S is near the intersection of this altitude layer and the singular curve, the direction of this intersection is generally perpendicular to the radial vector direction from the observation platform P to the center of the Earth O. When the camera is pointed at the target S according to the traditional orbit normal direction, the two real number solutions obtained after Gaussian orbit determination of the acquired observation data will be highly close. In this case, although the tendency of the two solutions to coincide can simplify the multi-solution problem from a mathematical perspective, in actual observations, due to observation errors and the approximation of the target position relationship model, two numerically close orbit solutions are still obtained, and it is difficult to accurately distinguish between the true solution and the false solution within the limited orbit arc segment.

[0159] In order to improve the separation capability of the Gaussian orbit determination method in such scenarios, a camera line of sight selection strategy is further proposed, that is, in the camera observation planning, the direction where the observation altitude layer intersects the singular curve is preferentially avoided. Figure 10B In the figure, the pink dotted line represents the changing trajectory of the sight direction strategy. When the observation sight moves away from the singular intersection direction, the difference between the two solutions is more obvious, thereby improving the discrimination of the solutions.

[0160] According to the above embodiment, after adopting the above camera pointing optimization strategy, the solution spacing under the Gaussian orbit determination method can be significantly expanded. Figure 10B As shown, the blue and red trajectories are clearly distinguishable, making it possible to effectively determine which solution represents the target's true trajectory, even within the observation range of a short trajectory segment. Furthermore, the angular difference between the camera's actual pointing direction and the singular direction can be used to infer the reliability of the current solution. The greater the deviation, the more reliable the solution; the smaller the deviation, the less reliable the solution.

[0161] In some embodiments, as Figure 5 As shown, step 103 includes steps 501 to 502.

[0162] Step 501: Determine target orbit parameters according to the initial observation time t1, the first target position vector, the final observation time t3 and the third target position vector.

[0163] In an embodiment of the present invention, the Gooding Orbit Determination Method uses the distance of the target S relative to the observation platform P at the initial observation time and the distance of the target S relative to the observation platform P at the terminal observation time as the variables to be determined. According to the position vector of the target S at the initial observation time and the terminal observation time relative to the center of the earth O at different observation times, the Lambert orbit transfer algorithm is used to calculate the orbit trajectory, and then the direction information of the target S at the intermediate observation time is estimated. The estimated direction is compared with the actual observation direction at the intermediate observation time. According to the deviation between the two, the actual values ​​of the distance ρ1 of the target S relative to the observation platform P at the initial observation time and the distance ρ3 of the target S relative to the observation platform P at the terminal observation time are inferred to determine the target orbit parameters.

[0164] Step 502: Perform perturbation compensation based on the target orbit parameters to obtain a predicted target orbit.

[0165] In an embodiment of the present invention, since the target orbit in the actual space environment is affected by multiple non-ideal factors, such as the Earth's non-spherical gravitational field, three-body perturbations, atmospheric drag, and solar radiation pressure, the target orbit parameters obtained solely based on the ideal two-body model are difficult to truly reflect the target's actual motion state. Therefore, after obtaining the target orbit parameters, the target orbit is further corrected based on the J2 perturbation dynamics model. The target orbit parameters are input into the dynamics model containing the perturbation term through the orbit propagation method, and the target position and velocity at different times are iteratively updated to obtain the corrected predicted target orbit.

[0166] According to the above embodiment, by introducing the Gooding orbit determination method, the target position vector corresponding to the initial observation time and the final observation time is used as input, and the direction information of the intermediate observation time is inverted and estimated in combination with the Lambert orbit transfer algorithm, thereby accurately estimating the distance of the target relative to the observation platform at the initial observation time and the final observation time and determining the target orbit parameters. The above method does not need to rely on the initial value of the target velocity, which effectively improves the applicability of the orbit determination process and the stability of the initial conditions. In addition, in the case where the target's true orbit is affected by perturbation factors such as the non-spherical gravitational field of the earth, the target orbit parameters calculated based on the two-body dynamics model are corrected by introducing the J2 perturbation model, which significantly enhances the ability of the orbit propagation result to fit the actual orbital motion state. The above method improves the physical accuracy and engineering applicability of the orbit solution while ensuring computational efficiency.

[0167] In some embodiments, as Figure 6 As shown, step 501 includes steps 601 to 603.

[0168] Step 601: Determine initial orbit parameters based on the initial observation time, the first target position vector, the end observation time, and the second target position vector.

[0169] In the embodiment of the present invention, the position vector r1 of the target S relative to the center of the earth O at the initial observation time t1, the final observation time t3, and the position vector r3 of the target S relative to the center of the earth O at the final observation time obtained by the Gaussian orbit determination method are input into the Lambert transfer function to construct the transfer orbit of the target S within the observation time interval, and obtain a set of initial orbital parameters corresponding to the target S. The initial orbital parameters include: the semi-major axis a of the transfer orbit o , the eccentricity e of the transfer orbit o 、Orbital inclination (Inclination) i o , right ascension of the ascending node (RAAN) Ω o 、Argument of Perigee ω o 、True Anomaly f o . Among them, the orbital inclination i o Indicates the inclination of the orbital plane relative to the equatorial plane, the right ascension of the ascending node Ω o Indicates the direction angle of the intersection of the orbital plane and the Earth's equatorial plane on the equatorial plane, the argument of perigee ω o The true anomaly angle f is the angle from the ascending node to the perigee in the orbital plane. o Indicates the current position of the target on the track.

[0170] Step 602: Determine the target direction prediction value corresponding to the intermediate observation time based on the initial orbit parameters, and compare the target direction prediction value with the unit position vector of the observation platform at the intermediate observation time. The target direction prediction value is the predicted unit position vector L2 of the target S relative to the observation platform P at the intermediate observation time. ’ .

[0171] In this embodiment of the present invention, after obtaining the initial orbital parameters, the position and velocity of the target S at any observation time are calculated using the classical orbital mechanics model (such as the Kepler motion or perturbation model) in the orbit propagation method. That is, the predicted position vector r2 of the target S relative to the center of the Earth O at the intermediate observation time is calculated using a standard orbit propagator (such as the poliastro module in Python). ’ .

[0172] The predicted position vector r2 of the target S relative to the center of the earth O at the intermediate observation time ’Substitute the position vector Rc2 of the observation platform P relative to the center of the earth O at the intermediate observation time into the following formula (20) to calculate the predicted unit position vector L2 of the target S relative to the observation platform P at the intermediate observation time ’ .

[0173]

[0174] Among them, r2 ’ is the predicted position vector of the target S relative to the center of the earth O at the intermediate observation moment, and Rc2 is the position vector of the observation platform P relative to the center of the earth O at the intermediate observation moment.

[0175] The predicted unit position vector L2 of the target S relative to the observation platform P at the intermediate observation time ’ Compare with the unit position vector L2 of the target S relative to the observation platform P at the intermediate observation moment.

[0176] If L2 ’ = L2 (or L2 ’ The error between L2 and the observation platform P is within the preset threshold range), indicating that the distance ρ1 of the target S relative to the observation platform P at the initial observation time and the distance ρ3 of the target S relative to the observation platform P at the end of the observation time calculated by the Gaussian orbit determination algorithm are accurate. 1真 ,ρ3 as ρ 3真 .

[0177] Step 603: If the error between the target direction prediction value and the unit position vector of the observation platform at the intermediate observation time exceeds a preset threshold range, the target orbit parameters are determined according to the target direction prediction value.

[0178] According to the above embodiment, by combining the Gaussian orbit determination method with the Lambert orbit transfer algorithm, a transfer orbit model is constructed based on the target position vectors at the initial and final observation times, thereby deriving the target's initial orbital parameter set. Based on these initial orbital parameters, the orbit propagation method is used to calculate the target's predicted position and direction at intermediate observation times, achieving a precise estimation of the target's direction at these intermediate observation times. By comparing the predicted direction with the actual observed direction at the intermediate observation time, the validity of the current orbital parameters is determined, making the orbit determination process self-verifying and effectively improving the stability and reliability of the orbital parameter inversion.

[0179] In some embodiments, as Figure 7 As shown, step 603 includes steps 701 to 702.

[0180] Step 701: Establish a nonlinear trajectory model based on the target direction prediction value to obtain the optimized distance ρ of the target relative to the observation platform at the initial observation time 1opt And the distance ρ of the target relative to the observation platform at the end of observation3opt .

[0181] In the embodiment of the present invention, the predicted unit position vector L2 of the target S relative to the observation platform P at the intermediate observation moment obtained by the first calculation is used. 1 The projection direction on normal plane n is defined as the x-direction, and the direction orthogonal to this projection direction within plane n is defined as the y-direction. Plane n is the projection plane determined by the unit position vector L2 of the target S relative to the observation platform P at the intermediate observation time as the normal vector.

[0182] The predicted unit position vector L2 of the target S relative to the observation platform P at the intermediate observation time ’ Projecting onto plane n, we get L2 ’ The projection components in plane n are denoted as F and G respectively.

[0183] Based on the above projection components, the nonlinear equation system (21) is constructed as follows:

[0184]

[0185] Among them, ρ1 is the distance between the target S and the observation platform P at the initial observation time, and ρ3 is the distance between the target S and the observation platform P at the end of the observation time.

[0186] Based on the above nonlinear equations, the partial derivatives are obtained by numerical gradient calculation (such as finite difference method), and the two-dimensional Newton method is used to iteratively solve ρ1 and ρ3. When the solution of the above nonlinear equations converges, the distance ρ of the target relative to the observation platform at the optimized initial observation time can be obtained. 1opt And the distance ρ of the target relative to the observation platform at the end of observation 3opt .

[0187] Step 702: Based on the optimized distance ρ between the target and the observation platform at the initial observation time 1opt And the distance ρ of the target relative to the observation platform at the end of observation 3opt Determine the optimized target orbit parameters.

[0188] In the embodiment of the present invention, the position vector Rc1 of the observation platform P relative to the center of the earth O at the initial observation time, the unit position vector L1 of the target S relative to the observation platform P at the initial observation time, and the optimized distance ρ of the target relative to the observation platform at the initial observation time are calculated. 1opt The position vector Rc3 of the observation platform P relative to the center of the earth O at the time of termination of observation, the unit position vector L3 of the target S relative to the observation platform P at the time of termination of observation, and the distance ρ of the target relative to the observation platform at the time of termination of observation after optimization. 3optSubstitute the above two sets of data into the above formula (1) to calculate the optimized initial observation time target S relative to the center of the earth O position vector r 1opt and the position vector r of the target S relative to the center of the earth O at the time of termination of observation 3opt .

[0189] The optimized initial observation time target S relative to the center of the earth O is obtained by solving the initial observation time t1, the final observation time t3, and the Gooding method. 1opt and the position vector r of the target S relative to the center of the earth O at the time of termination of observation 3opt Input into the Lambert transfer function, reconstruct the target orbit of target S in the observation time interval, and obtain a set of target orbit parameters (a opt , e opt ,i opt ,Ω opt ,ω opt , f opt ).

[0190] According to the above-described embodiment, by introducing the Gooding orbit determination method and combining it with the Lambert transfer algorithm, the orbital parameters of the target can be accurately constructed and optimized based solely on the spatial geometric relationships and corresponding unit position vectors at multiple observation times, without relying on the target's initial velocity information. By establishing the target's position vector relative to the center of the Earth at the initial and final observation times, and using orbital propagation methods to infer the target's predicted position at intermediate observation times, and further comparing this predicted position with the actual observation data at the intermediate observation times, a set of nonlinear constraint equations is constructed to inversely infer the target's true distance from the observation platform at the initial and final observation times, thereby improving the accuracy and physical rationality of the orbit estimation results. Based on this set of nonlinear equations, a numerical optimization method is used to dynamically correct the initial input values ​​of the Gaussian orbit determination algorithm, effectively improving the numerical stability and computational accuracy of the orbit parameter solution.

[0191] During actual target motion, the target is affected by various perturbations. Even if the target direction prediction value is highly consistent with the actual observed azimuth, the predicted target orbit may deviate from the true orbit. Therefore, in order to improve the accuracy and physical consistency of orbit estimation, the embodiments of the present invention improve the above-mentioned Gooding orbit determination algorithm. Given that the derivation of the target direction prediction value is based on an idealized two-body dynamics model, in order to fit the difference between the two-body dynamics model and the actual situation, the unit position vector of the target relative to the observation platform obtained by actual observation is corrected to an ideal azimuth under the influence of only the central gravity. The obtained corrected unit position vector is more consistent with the assumptions of the two-body dynamics model and can be used as an input parameter of the improved Gooding algorithm. Therefore, when the target direction prediction value is consistent with the corrected unit position vector, it can be ensured that the target orbit parameters calculated based on the direction prediction result are closer to the true orbit, thereby effectively compensating for the impact of perturbation errors on the orbit determination results.

[0192] In some embodiments, as Figure 8 As shown, step 502 includes steps 801 to 805.

[0193] Step 801: Perform perturbation compensation based on the optimized target orbit parameters, the two-body dynamics model, and the J2 perturbation dynamics model to obtain a perturbation error.

[0194] Step 802: Determine the perturbation deviation based on the optimized distance of the target relative to the observation platform and its corresponding perturbation error .

[0195] In the embodiment of the present invention, the initial observation time t1, the intermediate observation time t2, the final observation time t3, the distance ρ of the target relative to the observation platform at the optimized initial observation time 1opt And the distance ρ of the target relative to the observation platform at the end of observation 3opt , substitute into the following formula (22) to calculate the distance ρ of the target relative to the observation platform at the optimized intermediate observation time 2opt .

[0196]

[0197] Among them, ρ 1opt is the distance between the target and the observation platform at the optimized initial observation time, ρ 3opt is the distance between the target and the observation platform at the optimized end observation time, t1 is the initial observation time, t2 is the intermediate observation time, and t3 is the end observation time.

[0198] The perturbation error δr1 and its corresponding optimized initial observation time target relative to the observation platform distance ρ 1opt, the perturbation error δr2 and its corresponding optimized distance ρ from the target to the observation platform at the intermediate observation moment 2opt , the perturbation error δr3 and its corresponding optimized distance ρ from the target to the observation platform at the end of observation 3opt Substitute the three data pairs into formula (23) to calculate the perturbation deviation δL corresponding to different observation times t .

[0199]

[0200] in, is the perturbation error at any observation time, ρ topt The distance between the target and the observation platform at the optimized termination time of any observation time.

[0201] Step 803: Determine a corrected unit position vector of the target relative to the observation platform based on the perturbation deviation and the unit position vector of the target relative to the observation platform.

[0202] In the embodiment of the present invention, the perturbation error δr2 and its corresponding unit position vector L1 of the target S relative to the observation platform P at the initial observation time, the perturbation error δr2 and its corresponding unit position vector L2 of the target S relative to the observation platform P at the intermediate observation time, and the perturbation error δr3 and its corresponding unit position vector L3 of the target S relative to the observation platform P at the final observation time are substituted into formula (24) to calculate the corrected unit position vector L of the target S relative to the observation platform P corresponding to different observation times. t修正 .

[0203]

[0204] Step 804: Determine the orbit based on the corrected unit position vector of the target relative to the observation platform.

[0205] In the embodiment of the present invention, the corrected unit position vector L of the target S relative to the observation platform P at different observation times is t修正 And the corresponding optimized distance ρ of the target S relative to the observation platform P 2opt and the position vector of the observation platform P relative to the center of the earth O are substituted into formula (1) to calculate the corrected unit position vector r of the target S relative to the center of the earth O at different observation times. t修正 .

[0206] The initial observation time t1, the end observation time t3, the corrected initial observation time target S relative to the center of the earth O unit position vector r 1修正 and the unit position vector r of the target S relative to the center of the earth O at the time of termination of observation 3修正Input into the Lambert transfer function, construct the transfer orbit of target S in the observation time interval, and obtain a set of corrected orbital parameters corresponding to target S.

[0207] Step 805: Iterate steps 801 to 804 until a preset number of times is reached or convergence is achieved, and obtain the corrected target orbit parameters.

[0208] According to the above-described embodiment, by introducing a perturbation compensation mechanism and integrating an orbital dynamics model including the J2 perturbation term into the traditional Gooding orbit determination algorithm, the physical accuracy and dynamic stability of the orbit solution are significantly improved. Given that target orbits in real space environments are often subject to interference from non-ideal factors such as the Earth's non-spherical gravitational field, atmospheric drag, and solar radiation pressure, relying solely on the traditional two-body dynamics model cannot accurately reflect the target's true motion state. Therefore, after obtaining the optimized target orbit parameters, orbit propagation is performed based on both the ideal two-body model and the dynamics model including the J2 perturbation term to obtain the corresponding predicted target orbit state. The perturbation error is then constructed using the difference between the two. Based on this, the unit position vector and corresponding distance of the target relative to the observation platform are corrected to compensate for the perturbation deviation of the original observation input, thereby updating the target's position vector relative to the center of the Earth and the target orbit parameters. By iteratively executing this compensation process, the target orbit solution can gradually approach the true physical orbit state, significantly improving the adaptability and accuracy of the orbit determination algorithm in complex space environments.

[0209] In some embodiments, as Figure 9 As shown, step 801 includes steps 901 to 903.

[0210] Step 901: Determine the velocity vector at the initial observation time based on the optimized target orbit parameters.

[0211] In the embodiment of the present invention, after obtaining the target orbit parameters, the position and velocity of the target S at any observation time are calculated using the classical orbital mechanics model (such as Kepler motion or perturbation model) in the orbit propagation method. That is, the velocity vector v of the target S at the initial observation time t1 is calculated using a standard orbit propagator (such as the poliastro module in Python). 1opt .

[0212] Step 902: Numerical integration is performed based on the velocity vector at the initial observation time and its corresponding position vector, the two-body dynamics model, and the J2 perturbation dynamics model to obtain the predicted target position vector and the J2 perturbation predicted target position vector at different observation times.

[0213] In the embodiment of the present invention, the orbital motion follows the orbital dynamics differential equation (i.e., the two-body dynamics model), and the position vector r of the target S relative to the center of the earth O at the optimized initial observation time is1opt and its corresponding velocity vector v of target S at the initial observation time t1 1opt Input into the two-body dynamics model, use the numerical integration method (you can call the scipy.integrate.solve_ivp function in Python or the propagate function of the poliastro module) to solve the orbital dynamics differential equation, and based on this initial state, gradually propagate the orbit of the target S to obtain the predicted target position vector r at any observation time. t , in order to realize the timing calculation and dynamic tracking of the target orbital state.

[0214] The two-body dynamics model is shown in the following formula (25):

[0215]

[0216] in, is the acceleration vector of target S, r is the position vector of target S relative to the center of the earth O, μ is the standard gravitational constant of the earth, and r is the modulus of the position vector of target S relative to the center of the earth O.

[0217] The orbital motion follows the orbital dynamics differential equation containing the J2 perturbation term (i.e., the J2 perturbation dynamics model), and the position vector r of the target S relative to the center of the earth O at the optimized initial observation time is 1opt and its corresponding velocity vector v of target S at the initial observation time t1 1opt Input into the J2 perturbation dynamics model, use the numerical integration method (you can call the scipy.integrate.solve_ivp function in Python or the propagate function of the poliastro module) to solve the orbital dynamics differential equation containing the J2 perturbation term, and gradually propagate the orbit of the target S based on this initial state to obtain the J2 perturbation predicted target position vector r at any observation time tJ2 , in order to realize the timing calculation and dynamic tracking of the target orbital state.

[0218] The J2 perturbation dynamics model is shown in the following formula (26):

[0219]

[0220] in, is the acceleration vector of target S, r is the position vector of target S relative to the center of the earth O, μ is the standard gravitational constant of the center of the earth, r is the modulus of the position vector of target S relative to the center of the earth O, F J2 is the perturbation acceleration component, F J2 It can be expressed as .

[0221] According to the following formulas (27), (28) and (29), F is calculated respectively. J2 The component of the perturbation acceleration in the x direction F J2x 、F J2 The component of the perturbation acceleration in the y direction F J2y and F J2 The component of the perturbation acceleration in the z direction is F J2z .

[0222]

[0223] Where μ is the standard gravitational constant of the Earth’s center, R e is the equatorial radius of the Earth, J2 is the second non-spherical harmonic gravitational coefficient of the Earth (i.e., the J2 term), r is the modulus of the position vector of the target S relative to the center of the Earth O, z is the z component of the position vector of the target S in the geocentric inertial coordinate system, and x is the x component of the position vector of the target S in the geocentric inertial coordinate system.

[0224]

[0225] Where μ is the standard gravitational constant of the Earth’s center, R e is the equatorial radius of the Earth, J2 is the second non-spherical harmonic gravitational coefficient of the Earth (i.e., the J2 term), r is the modulus of the position vector of the target S relative to the center of the Earth O, z is the z component of the position vector of the target S in the geocentric inertial coordinate system, and y is the y component of the position vector of the target S in the geocentric inertial coordinate system.

[0226]

[0227] Where μ is the standard gravitational constant of the Earth’s center, R e is the equatorial radius of the Earth, J2 is the second non-spherical harmonic gravitational coefficient of the Earth (i.e., the J2 term), r is the modulus of the position vector of the target S relative to the center of the Earth O, and z is the z component of the position vector of the target S in the Earth-centered inertial coordinate system.

[0228] Step 903: Based on the predicted target position vector r t and J2 perturbation predicted target position vector r tJ2 Determine the perturbation error δr t .

[0229] In the embodiment of the present invention, the predicted target position vector r t and J2 perturbation predicted target position vector r tJ2 Substitute into the following formula (30) to calculate the perturbation error δr t .

[0230]

[0231] Among them, rt is the predicted target position vector at any observation time, r tJ2 Predict the target position vector for the J2 perturbation at any observation time.

[0232] According to the above embodiment, based on the obtained target orbit parameters, the target orbit is propagated using a two-body dynamics model and a J2 perturbation dynamics model, respectively. An orbital state evolution process that takes perturbation factors into account is constructed, thereby more comprehensively simulating the motion characteristics of the target in the actual space environment. The predicted position vectors are obtained without and with perturbation effects, respectively, through numerical integration methods. The perturbation error between the two is calculated based on this, achieving a quantitative assessment of the impact of the perturbation term. This method not only improves the physical accuracy and dynamic controllability of orbital state estimation, but also provides an accurate and reliable model basis for subsequent orbit determination error compensation and trajectory correction, effectively enhancing the stability and robustness of the entire orbit determination system.

[0233] To further reduce the impact of observation errors on orbit determination accuracy, some embodiments of the present invention also provide a screening strategy based on semi-major axis differences. This strategy analyzes the differences between the semi-major axis parameters calculated from different observation data to select valid samples with good convergence and consistency from multiple orbit determination results, eliminating anomalous results with large deviations due to observation errors. This significantly reduces orbit determination errors and improves the accuracy and stability of orbit determination results.

[0234] The three sets of observation data are acquired, keeping the intermediate observation time constant. The initial and final observation times are time-perturbed, shifting them forward or backward by 0.4 seconds, 0.8 seconds, 1.2 seconds, 1.6 seconds, and 2 seconds, respectively, relative to the intermediate observation time. This constructs six sets of observation data for different time segments. The six sets of observation data are then subjected to orbit determination using the improved Gooding orbit determination method, obtaining six consecutive orbital parameters for the same observation segment as the orbit determination result set for that segment. Based on this orbit determination result set, the semi-major axis values ​​of the transfer orbits are extracted from the six sets of orbital parameters, and the maximum difference between these values ​​is calculated. If this maximum difference exceeds a preset threshold, the observation segment is deemed to have significant error and is discarded. The setting of the preset threshold should be determined based on the data characteristics of the actual orbit determination mission and can be selected based on simulation results, but the present invention is not limited to this.

[0235] In another embodiment of the present application, a low-orbit target orbit determination device is also provided.

[0236] An embodiment of the present application provides a low-orbit target orbit determination device, which is applied / configured to a terminal device. The low-orbit target orbit determination device and the low-orbit target orbit determination method in one embodiment of the present application are based on the same inventive concept and have similar principles for solving problems. Therefore, the implementation of the low-orbit target orbit determination device refers to the implementation of the low-orbit target orbit determination method in one embodiment of the present application, and the repeated parts will not be repeated. As used below, the terms "unit" or "module" can be a combination of software and / or hardware that implements predetermined functions. Although the system described in the following embodiments is preferably implemented in software, implementation in hardware, or a combination of software and hardware, is also possible and conceived.

[0237] like Figure 11 As shown, the low-orbit target orbit determination device 1100 includes: an observation data acquisition module 1101, a target position calculation module 1102 and an orbit prediction module 1103.

[0238] The observation data acquisition module 1101 is used to acquire observation data at different times, wherein the observation data includes: a first position vector of the observation platform relative to the center of the earth and a second position vector of the target relative to the observation platform.

[0239] The target position calculation module 1102 is used to determine the target position vector based on the observation data and a pre-established target position relationship model. The target position vector includes a first target position vector corresponding to the initial observation time, a second target position vector corresponding to the intermediate observation time, and a third target position vector corresponding to the final observation time. The target position relationship model is determined based on the second target position vector and the first position vector.

[0240] The orbit prediction module 1103 is used to determine the predicted target orbit according to the initial observation time, the first target position vector, the end observation time and the third target position vector.

[0241] In some embodiments, the target position calculation module 1102 includes: an intermediate time distance calculation unit, a target distance estimation unit, and a position vector determination unit.

[0242] The intermediate moment distance solving unit is used to determine the first distance of the target relative to the center of the earth at the intermediate observation moment based on the target position relationship model.

[0243] The target distance estimation unit is used to determine the third distance based on the first distance, the second distance of the observation platform relative to the center of the earth at the intermediate observation time, the angle between the target and the line connecting the center of the earth and the observation platform, the first position vector and the weight factor.

[0244] The position vector determining unit is used to determine the target position vector according to the position vector of the observation platform relative to the center of the earth, the unit position vector of the target relative to the observation platform, and the distance of the target relative to the observation platform.

[0245] In some embodiments, the intermediate time distance calculation unit includes: a position vector determination unit, a structure coefficient calculation subunit and an intermediate distance calculation subunit.

[0246] The parameter extraction subunit is used to determine the normalized scale adjustment factor and the observation decoupling proportional coefficient based on the observation data.

[0247] The structure coefficient calculation subunit is used to determine the first orbit structure coefficient, the second orbit structure coefficient and the third orbit structure coefficient according to the normalized scale adjustment factor and the observation decoupling proportional coefficient.

[0248] The intermediate distance calculation subunit is used to determine the first distance according to the first track structure coefficient, the second track structure coefficient, the third track structure coefficient and the target position relationship model.

[0249] In some embodiments, the third distance includes: a fourth distance of the target relative to the observation platform at the initial observation time, a fifth distance of the target relative to the observation platform at the intermediate observation time, and a sixth distance of the target relative to the observation platform at the final observation time. The weighting factor includes a first weighting factor and a second weighting factor.

[0250] The target distance estimation unit includes: an intermediate distance derivation subunit and a time weight estimation subunit.

[0251] The intermediate distance derivation subunit is used to determine the fifth distance according to the first distance, the second distance and the angle between the target and the line connecting the center of the earth and the observation platform.

[0252] The time weight estimation subunit is configured to determine a fourth distance and a sixth distance according to the first position vector, the second position vector, the first weight factor, the second weight factor, and the fifth distance.

[0253] In some embodiments, the orbit prediction module 1103 includes: an orbit parameter determination unit and a perturbation compensation unit.

[0254] The orbit parameter determination unit is used to determine the target orbit parameter according to the initial observation time, the first target position vector, the end observation time and the third target position vector.

[0255] The perturbation compensation unit is used to perform perturbation compensation processing based on the target orbit parameters to obtain a predicted target orbit.

[0256] In some embodiments, the orbit parameter determination unit includes: an initial orbit calculation subunit, a prediction value calculation subunit, and an orbit parameter optimization subunit.

[0257] The initial orbit calculation subunit is used to determine the initial orbit parameters according to the initial observation time, the first target position vector, the end observation time and the second target position vector.

[0258] The prediction value calculation subunit is used to determine the target direction prediction value corresponding to the intermediate observation time according to the initial orbit parameters, and compare the target direction prediction value with the unit position vector of the observation platform at the intermediate observation time.

[0259] The orbit parameter optimization subunit is used to determine the target orbit parameters according to the target direction prediction value if the error between the target direction prediction value and the unit position vector of the observation platform at the intermediate observation time exceeds a preset threshold range.

[0260] In some embodiments, the trajectory parameter optimization subunit includes: a nonlinear modeling subunit and a parameter updating subunit.

[0261] The nonlinear modeling subunit is used to establish a track nonlinear model based on the target direction prediction value to obtain the optimized fourth distance and sixth distance.

[0262] The parameter updating subunit is used to determine optimized target orbit parameters according to the optimized fourth distance and sixth distance.

[0263] In some embodiments, the perturbation compensation unit includes: a perturbation error acquisition subunit, a perturbation deviation determination subunit, a unit vector correction subunit, a trajectory reconstruction subunit, and a trajectory convergence iteration subunit.

[0264] The perturbation error acquisition subunit is used to perform perturbation compensation based on the optimized target orbit parameters, the two-body dynamics model and the J2 perturbation dynamics model to obtain the perturbation error.

[0265] The perturbation deviation determining subunit is configured to determine the perturbation deviation according to the optimized third distance and its corresponding perturbation error.

[0266] The unit vector correction subunit is used to determine a corrected second position vector according to the perturbation deviation and the second position vector.

[0267] The orbit reconstruction subunit is used to determine the orbit based on the corrected second position vector.

[0268] The orbit convergence iteration subunit is used to iteratively execute the above steps until a preset number of times is reached or convergence is achieved, thereby obtaining the corrected target orbit parameters.

[0269] In some embodiments, the perturbation error acquisition subunit includes: a velocity estimation subunit, an integral propagation subunit, and an error solution subunit.

[0270] The velocity calculation subunit is used to determine the velocity vector at the initial observation time based on the optimized target orbit parameters.

[0271] The integral propagation subunit is used to perform numerical integration based on the velocity vector at the initial observation time and its corresponding position vector, the two-body dynamics model and the J2 perturbation dynamics model to obtain the predicted target position vector at different observation times and the J2 perturbation predicted target position vector.

[0272] The error solving subunit is used to determine the perturbation error based on the predicted target position vector and the J2 perturbation predicted target position vector.

[0273] Figure 12 A schematic diagram of the physical structure of an electronic device provided in an embodiment of the present invention, such as Figure 12 As shown, the electronic device 1200 includes a processor 1201 , a memory 1202 and a bus 1203 .

[0274] The processor 1201 and the memory 1202 communicate with each other via a bus 1203 .

[0275] The processor 1201 is configured to call program instructions in the memory 1202 to execute the methods provided by the above-mentioned method embodiments.

[0276] An embodiment of the present invention further provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the above-mentioned low-orbit target orbit determination method is implemented.

[0277] An embodiment of the present invention further provides a computer program product, which includes a computer program. When the computer program is executed by a processor, it implements the above-mentioned low-orbit target orbit determination method.

[0278] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0279] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, such that the instructions, when executed by the processor of the computer or other programmable data processing device, produce means for implementing the functions specified in one or more processes in the flowcharts and / or one or more blocks in the block diagrams.

[0280] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce a product including an instruction device that implements the functions specified in one or more processes in the flowchart and / or one or more boxes in the block diagram.

[0281] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more processes in the flowchart and / or one or more boxes in the block diagram.

[0282] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for determining the orbit of a low-orbit target, characterized in that: include: Acquire observation data at different times; wherein the observation data includes: a first position vector of the observation platform relative to the center of the earth and a second position vector of the target relative to the observation platform; Determining a target position vector based on the observation data and a pre-established target position relationship model; the target position vector includes a first target position vector corresponding to an initial observation time, a second target position vector corresponding to an intermediate observation time, and a third target position vector corresponding to a final observation time; the target position relationship model is determined based on the second target position vector and the first position vector; Determining a predicted target trajectory based on the initial observation time, the first target position vector, the termination observation time, and the third target position vector; Determining the predicted target orbit based on the initial observation time, the first target position vector, the end observation time, and the third target position vector includes: determining target orbit parameters based on the initial observation time, the first target position vector, the end observation time, and the third target position vector; performing perturbation compensation processing based on the target orbit parameters to obtain the predicted target orbit; The determining of the target orbit parameters based on the initial observation time, the first target position vector, the termination observation time and the third target position vector includes: determining the initial orbit parameters based on the initial observation time, the first target position vector, the termination observation time and the second target position vector; determining the target direction prediction value corresponding to the intermediate observation time based on the initial orbit parameters, and comparing the target direction prediction value with the unit position vector of the observation platform at the intermediate observation time; if the error between the target direction prediction value and the unit position vector of the observation platform at the intermediate observation time exceeds a preset threshold range, determining the target orbit parameters based on the target direction prediction value.

2. The method according to claim 1, characterized in that Determining the target position vector according to the observation data and a pre-established target position relationship model includes: Determining a first distance of the target relative to the center of the earth at an intermediate observation moment based on the target position relationship model; determining a third distance based on the first distance, a second distance of the observation platform relative to the center of the earth at the intermediate observation moment, an angle between the target and a line connecting the center of the earth and the observation platform, the first position vector, and a weight factor; The target position vector is determined according to the first position vector, the second position vector, and the third distance.

3. The method according to claim 2, characterized in that Determining a first distance of the target relative to the center of the earth at the intermediate observation moment based on the target position relationship model includes: Determining a normalized scale adjustment factor and an observation decoupling proportional coefficient based on the observation data; Determining a first orbital structure coefficient, a second orbital structure coefficient, and a third orbital structure coefficient according to the normalized scale adjustment factor and the observation decoupling proportional coefficient; The first distance is determined according to the first track structure coefficient, the second track structure coefficient, the third track structure coefficient and the target position relationship model.

4. The method according to claim 2, characterized in that The third distance includes: a fourth distance of the target relative to the observation platform at the initial observation time, a fifth distance of the target relative to the observation platform at the intermediate observation time, and a sixth distance of the target relative to the observation platform at the end observation time; the weight factor includes a first weight factor and a second weight factor; Determining the third distance according to the first distance, the second distance, the angle between the target and a line connecting the center of the earth and the observation platform, the first position vector, and a weight factor includes: determining the fifth distance based on the first distance, the second distance, and an angle between the target and a line connecting the center of the earth and the observation platform; The fourth distance and the sixth distance are determined according to the first position vector, the second position vector, the first weight factor, the second weight factor, and the fifth distance.

5. The method according to claim 4, characterized in that The determining the target orbit parameter according to the target direction prediction value includes: Establishing a nonlinear track model based on the target direction prediction value to obtain an optimized fourth distance and a sixth distance; Optimized target orbit parameters are determined based on the optimized fourth distance and sixth distance.

6. The method according to claim 5, characterized in that The performing perturbation compensation processing based on the target orbit parameters to obtain a predicted target orbit includes: Perturbation compensation is performed based on the optimized target orbit parameters, two-body dynamics model and J2 perturbation dynamics model to obtain the perturbation error; determining a perturbation deviation according to the optimized third distance and its corresponding perturbation error; determining a corrected second position vector according to the perturbation deviation and the second position vector; performing orbit determination based on the corrected second position vector; The above steps are iterated until the preset number of times is reached or convergence is achieved, and the corrected target orbit parameters are obtained.

7. The method according to claim 6, characterized in that The perturbation compensation is performed according to the optimized target orbit parameters, the two-body dynamics model and the J2 perturbation dynamics model to obtain the perturbation error, including: Determine the velocity vector at the initial observation time according to the optimized target orbit parameters; Based on the velocity vector at the initial observation time and its corresponding position vector, the two-body dynamics model and the J2 perturbation dynamics model, numerical integration is performed to obtain the predicted target position vector at different observation times and the J2 perturbation predicted target position vector; A perturbation error is determined based on the predicted target position vector and the J2 perturbation predicted target position vector.

8. A low-orbit target orbit determination device, characterized in that: include: An observation data acquisition module, configured to acquire observation data at different times; wherein the observation data includes: a first position vector of the observation platform relative to the center of the earth and a second position vector of the target relative to the observation platform; a target position calculation module, configured to determine a target position vector based on the observation data and a pre-established target position relationship model; the target position vector comprising a first target position vector corresponding to an initial observation time, a second target position vector corresponding to an intermediate observation time, and a third target position vector corresponding to a final observation time; the target position relationship model being determined based on the second target position vector corresponding to the intermediate observation time and the first position vector; a trajectory prediction module, configured to determine a predicted target trajectory based on the initial observation time, the first target position vector, the end observation time, and the third target position vector; The trajectory prediction module includes: an orbit parameter determination unit, configured to determine target orbit parameters based on the initial observation time, the first target position vector, the end observation time, and the third target position vector; a perturbation compensation unit, configured to perform perturbation compensation processing based on target orbit parameters to obtain a predicted target orbit; The orbit parameter determination unit includes: an initial orbit calculation subunit, configured to determine initial orbit parameters based on the initial observation time, the first target position vector, the end observation time, and the second target position vector; A prediction value calculation subunit is used to determine a target direction prediction value corresponding to an intermediate observation time according to the initial orbit parameters, and compare the target direction prediction value with the unit position vector of the observation platform at the intermediate observation time; The orbit parameter optimization subunit is used to determine the target orbit parameters according to the target direction prediction value if the error between the target direction prediction value and the unit position vector of the observation platform at the intermediate observation time exceeds a preset threshold range.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

11. A computer program product, characterized in that The computer program product comprises a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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